已知,x的2m+2n次方=8,x的3m-2n次方=4,求x的4m+6n次方

题目

已知,x的2m+2n次方=8,x的3m-2n次方=4,求x的4m+6n次方

答案

x^(2m+2n)*x^(3m-2n)=8*4
x^(2m+2n+3m-2n)=32
x^5m=2^5
(x^m)^5=2^5
x^m=2
x^(2m+2n)=8
x^2m*x^2n=8
(x^m)^2*x^2n=8
2^2*x^2n=8
x^2n=2
x^(4m+6n)
=x^(4m+4n)*x^2n
=[x^(2m+2n)]^2*x^2n
=8^2*2
=64*2
=128